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Abstract

The accuracy of the discrete dipole approximation (DDA) for computing forces and torques in optical trapping experiments is discussed in the context of dielectric spheres and a range of low symmetry particles, including particles with geometric anisotropy (spheroids), optical anisotropy (birefringent spheres) and structural inhomogeneity (core-shell spheres). DDA calculations are compared with the results of exact T-matrix theory. In each case excellent agreement is found between the two methods for predictions of optical forces, torques, trap stiffnesses and trapping positions. Since the DDA lends itself to calculations on particles of arbitrary shape, the study is augmented by considering more general systems which have received recent experimental interest. In particular, optical forces and torques on low symmetry letter-shaped colloidal particles, birefringent quartz cylinders and biphasic Janus particles are computed and the trapping behaviour of the particles is discussed. Very good agreement is found with the available experimental data. The efficiency of the DDA algorithm and methods of accelerating the calculations are also discussed.

(a) The equilibrium trapping height, zeqm, and (b) stiffness, kx, for dielectric spheres of radii r = 100,200,300 and 400nm, as a function of the DDA lattice parameter, δ. zeqm is measured from the focal plane.

(a) The equilibrium trapping height, zeqm, and (b) the translational stiffness kx, for dielectric spheres as a function of radius, for four values of the DDA lattice parameter, δ. The curves for δ ≥ 30nm are offset vertically, as they would otherwise be superimposed. (c) zeqm and (d) kx for dielectric spheres, comparing the DDA with δ = 15nm (black curves) and the T-matrix method (red curves), for three values of nm.

The forces and torques acting on silica letters, computed using the DDA. The dimensions are: ‘N’, 4 × 5μm; ‘A’, 3 × 4.6μm; ‘O’, 3 × 5μm. All letters have a thickness of 0.5μm in the y-direction, and lie in the xz-plane. (a) The y component of torque, τy, when rotating a letter ‘N’ about the y-axis through the two centres shown. (b) τy for rotation of a letter ‘A’ about the y-axis through the centre of the letter. (c) The x component of force, Fx, for a letter ‘O’ being translated parallel to the x-axis, for the two orientations shown. (d) A schematic illustration of the preferred trapping orientations of the three letters.

(a) The azimuthal stiffness,
Kzzrr, of homogeneous birefringent spheres in Gaussian beams as a function of sphere radius for several dielectric anisotropies, Δɛ. Calculations are performed using both T-matrix and DDA methods. (b) The azimuthal stiffness of quartz cylinders of various radii, as a function of length. The cylinders are oriented with long axes parallel to the beam axis. no = 1.544 parallel to the cylinder axis and ne = 1.553 parallel to a radius. Calculations were performed using the DDA method only.

(a) Schematic of the PTFE/silica core-shell spheres. (b) Equilibrium trapping heights and (c) trap stiffnesses for the core-shell spheres as a function of ra. (d) Expanded view of the rectangular region in part (c), plotted as a function of the shell thickness, rb – ra. In all cases, the shell radius, rb, is held constant at 0.75μm; the results from T-matrix and DDA calculations are compared.

The torques acting on biphasic Janus spheres, positioned at the focal point of a Gaussian beam, as a function of rotation angle about (a) the y-axis and (b) the x-axis. The accompanying lateral forces are shown for rotations about (c) the y-axis and (d) the x-axis. Calculations were performed using the DDA method, for spheres with radii in the range 0.3 to 0.7 μm. The refractive indices used were n1 = 1.05nm and n2 = 1.1nm.